It is generally agreed that children are able to acquire two languages to which they are exposed from birth as two L1s. Little attention has been drawn to cases when one language develops slower and is weaker in different aspects. A question under debate is whether the weaker language develops as an L2 rather than as an L1. The goal of this paper is to contribute to the understanding of the weaker language. This paper compares the acquisition of word order in the Italian DP by bilingual Italian/Swedish children with that of monolingual Italian children and Swedish adult second language learners of Italian. In this study there seems to exist a relationship between language dominance and the acquisition of word order in the DP in terms of N-raising. Non-target-like pre-nominal attributive adjectives and only pre-nominal possessives are observed in the Swedish-dominant bilingual child and the adults. The Italian-dominant child and the monolingual children position both types of adjectives target-like from the beginning. However, the preference for the pre-nominal position in the adults and the child with Italian as the weaker language occurs with different adjectives (obligatory post-nominal vs. variable adjectives). It is argued that transfer of the N-raising-parameter value in the adults and ambiguous input in the case of the child cause the preference for the pre-nominal adjectives.